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| It is not a logarithm to any particular base in the modern sense of the term, however, it can be rewritten as: | It is not a logarithm to any particular base in the modern sense of the term, however, it can be rewritten as: | ||
| <math>\mathrm{NapLog}(x) = \log_{\frac{10^7}{10^7 - 1}} 10^7 - \log_{\frac{10^7}{10^7 - 1}} x</math> | <math>\mathrm{NapLog}(x) = \log_{\frac{10^7}{10^7 - 1}} 10^7 - \log_{\frac{10^7}{10^7 - 1}} x</math> | ||
| and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one. | and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one. | ||
Revision as of 21:10, 29 November 2007
The Napierian logarithm, as first defined by John Napier, is a function which can be defined in terms of the modern logarithm by:
(Being a quotient of logarithms, the base of the logarithm chosen is irrelevant.)
It is not a logarithm to any particular base in the modern sense of the term, however, it can be rewritten as:
and hence it is a linear function of a particular logarithm, and so satisfies identities quite similar to the modern one.
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